Some properties that a thing has partially or wholly explain other properties the thing has or doesn’t have. For instance, my having a body partially explains my being in Waco and wholly explains my having a body or horns. Some properties that a thing has do not explain, even partially, what other properties the thing has or doesn’t have. Call such properties “explanatorily fundamental”.
So, here’s a theory. The primary essential properties of a thing are the explanatorily fundamental properties of the thing. The primary essential properties are both essential in the medieval explanatory sense and the contemporary modal sense (properties a thing cannot exist without).
What about the case of Christ, who is essentially divine and essentially human, and yet prior (in the order of explanation) to the incarnation was not human? Here’s what we could say: Divinity is the one and only primary essential property of Christ. But humanity is a secondary essential property. A secondary essential property of a thing is the sort of property that (a) is not a primary essential property of that thing, but (b) normally is the primary essential property of its possessor. In the case of Christ, his divinity is explanatorily prior to his humanity, but normally a thing’s humanity does not have any property of that thing explanatorily prior to it.
